Capacitance meter

ABSTRACT

A method for determining a flow property of a fluid flowing through a conduit ( 1 ) provided with a capacitance meter comprising an upstream and a downstream annular capacitance sensor ( 2   a,    2   b ), wherein each annular capacitance sensor comprises at least three sensor electrodes ( 11   a - 13   a,    11   b - 13   b ), which sensor electrodes are arranged around the circumference of the conduit, the method comprising selecting, for each annular capacitance sensor, a set of measurement capacitors, wherein a measurement capacitor is formed by two measurement electrodes, and wherein a measurement electrode consists either of a single sensor electrode or of at least two interconnected sensor electrodes; measuring at several moments during a time interval a capacitance of each measurement capacitor of each annular capacitance sensor ( 2   a,    2   b ); determining cross correlations between capacitances measured during the time interval at the upstream annular capacitance sensor ( 2   a ) and capacitances measured during the time interval at the downstream annular capacitance sensor ( 2   b ); and determining the flow property from the cross correlations.

[0001] The present invention relates to determining a property of afluid in a conduit using a capacitance meter.

[0002] Capacitance meters are used in the art to measure a dielectricproperty of a fluid. Often, based on one or more measurements of adielectric property, another property of the fluid can be determined.

[0003] A particular application of capacitance meters is in obtaining apictorial representation of a property of a fluid over a cross-sectionof the conduit, e.g. the dielectric constant or the spatial distributionof a particular component of a multi-component fluid. In thespecification the word ‘image’ is used to refer to such a pictorialrepresentation. A multi-component fluid is a fluid comprising more thanone component, for example a well fluid produced from an undergroundformation, which well fluid can comprise hydrocarbon oil, water, and/ornatural gas.

[0004] Methods that provide an image of the fluid based on capacitancemeasurements using a capacitance meter are often referred to ascapacitance tomography. Well known in the art are methods forcalculating an image from the capacitances measured by the capacitancemeter, for example linear back projection wherein the image iscalculated by a series of linear operations on the capacitances.

[0005] A capacitance meter for capacitance tomography is disclosed inEuropean patent specification with publication No. 0 326 266 B1. Theknown capacitance meter comprises an annular capacitance sensor arrangedaround a conduit. The capacitance sensor comprises eight sensorelectrodes, which are arranged around the circumference of the conduit.Capacitances between any two single sensor electrodes are measured,wherein each capacitance measurement samples an average dielectricconstant in the space probed by the respective electrodes. From themeasurements an image consisting of K pixels can be constructed, whereina pixel represents an average value of the dielectric constant in adiscrete space element in the cross-section, the pixel data. Such animage can be transformed into a concentration image or a density image.

[0006] If the fluid is flowing through the conduit, it is often highlydesirable obtain measurements of a flow property in addition to animage. In a publication by R. Thorn et al. in Flow Meas. Instrum. Vol.1, October 1990, pages 259-268, it has been disclosed, how a flowvelocity profile of the fluid can be obtained. To this end, thecapacitance meter comprises two annular capacitance sensors locatedupstream and downstream along the conduit. Using each annularcapacitance sensor, images P_(u) and P_(d) are determined repeatedlyduring a time interval. The flow velocity profile is determined fromcross correlations of pixel data P_(u,k) of images determined during thetime interval at the upstream sensor with pixel data P_(d,l) determinedduring the time interval at the downstream sensor. The cross correlationof pixel data, in the form of numbers representing for example density,can be described by${\left( {P_{u,k}*P_{d,l}} \right)(t)} = {\frac{1}{T}{\int_{0}^{T}{{P_{d,l}(s)}\quad {P_{u,k}\left( {t - s} \right)}{s}}}}$

[0007] wherein

[0008] k,l are integers, wherein 1≦k,l≦K and K is the number of pixelsin an image;

[0009] (P_(u,k)*P_(d,l))(t) is the cross correlation of pixel data at aselected time t;

[0010] P_(u,k)(t−s) is the number associated with pixel k of an imageprovided by the upstream sensor at time (t−s);

[0011] P_(d,l)(s) is the number associated with pixel 1 of an imageprovided by the downstream sensor at time s; and

[0012] T is the duration of a correlation time window during the timeinterval.

[0013] Note, that this and other equations in this specificationrelating to cross-correlation calculations are written in integral form;it will however be clear to the skilled person how to calculate crosscorrelations using discrete measurements.

[0014] The method described in the publication is referred to ascross-correlation capacitance tomography. If the fluid is amulti-component fluid, other flow properties such as the volumetric ormass flow rates of a particular component can be determined from aconcentration or density image and a flow velocity profile.

[0015] There are, however, a number of problems associated withcapacitance flow meters, that have so far hampered their practicalapplication in an industrial environment. For example, specificrequirements for applications in the oil industry, where the flow of amulti-component fluid is to be monitored, have not yet been met. Onerequirement relates to the speed of operation. For cross-correlationcapacitance tomography, processing of large amounts of data is required.

[0016] Consider the case that both the upstream and the downstreamcapacitance sensors contain N sensor electrodes. In known sensors N istypically in the order of 8 to 12. A complete data set of capacitancesmeasured between all pairs of single sensor electrodes at a singleannular capacitance sensor consists of in the order of N² measuredcapacitances (more precise N(N−1)/2 capacitances). From this data set animage is calculated consisting of in the order of (N²)²=N⁴ pixels. Todetermine a complete flow velocity profile, a large number of imagesneed to be determined during a time interval at both capacitancesensors, and all possible cross correlations between pixel data of eachimage plane must be calculated. This task requires then in the order ofN⁸ cross-correlation operations. This presents an immense computationalchallenge requiring high-performance data-processing devices, e.g.special purpose devices such as a parallel-processor. Thus, in theabsence of a far more efficient method for processing the data, the needfor high-performance data-processing devices will impede the practicalapplication in an industrial environment.

[0017] U.S. Pat. No. 5,396,806 discloses a method and apparatus fordetermining the mass-flow rate of a component in a two-component slurrymixture. The mass-flow rate is determined as the product of volumefraction of the component and overall flow velocity. The volume fractionis derived from the capacitance of the mixture, which capacitance ismeasured using a single annular capacitance sensor comprising a numberof electrodes. Measurements using different pairs of electrodes areaveraged in order to reduce the effects of non-uniformities of the flowpatterns. The flow velocity is derived from triboelectric measurements,by cross-correlation of signals measured by an upstream and a downstreamtriboelectric probe.

[0018] It is an object of the present invention to provide an efficientmethod and capacitance meter for determining a flow property of a fluidflowing through a conduit by using a capacitance flow meter.

[0019] A basis of the present invention is the insight gained byApplicant, that the efficiency of determining a flow velocity profile isstrongly determined by the number of cross-correlation calculations thatare necessary in cross-correlation capacitance tomography.

[0020] Applicant now has found that and how a considerable reduction ofthe number of cross-correlation calculations compared to the knownmethods can be achieved.

[0021] According to one aspect of the present invention there isprovided a method for determining a flow property of a fluid flowingthrough a conduit provided with a capacitance meter comprising anannular capacitance sensor, wherein the annular capacitance sensorcomprises at least three sensor electrodes, which sensor electrodes arearranged around the circumference of the conduit, the method comprisingthe steps of:

[0022] (a) selecting, for the annular capacitance sensor, a set ofmeasurement capacitors, wherein a measurement capacitor is formed by twomeasurement electrodes, and wherein a measurement electrode consistseither of a single sensor electrode or of at least two interconnectedsensor electrodes;

[0023] (b) measuring a capacitance of each measurement capacitor,characterized in that the annular capacitance sensor forms an upstreamannular capacitance sensor, and in that the capacitance meter furthercomprises a downstream annular capacitance sensor provided with at leastthree sensor electrodes, which sensor electrodes are arranged around thecircumference of the conduit, wherein the method further comprises thesteps of

[0024] (c) selecting, for the downstream annular capacitance sensor, aset of measurement capacitors;

[0025] (d) measuring at several moments during a time interval acapacitance of each measurement capacitor of each annular capacitancesensor;

[0026] (e) determining cross correlations between capacitances measuredduring the time interval at the upstream annular capacitance sensor andcapacitances measured during the time interval at the downstream annularcapacitance sensor; and

[0027] (f) determining the flow property from the cross correlations.

[0028] In this method according to the present invention first crosscorrelations between capacitances measured at an upstream sensor andcapacitances measured at a downstream sensor during a time interval arecalculated, and the flow property (e.g. a flow velocity profile) issubsequently determined from these cross correlations. If for thedetermination of the flow property cross correlations between pixel dataare needed, these cross correlations can be determined by linearoperation on the cross correlations between capacitances, wherein use ismade of a linear image calculation method. Accordingly, to determine thecomplete flow velocity profile, only in the order of (N²)²=N⁴ crosscorrelations need be determined, rather than N⁸ cross correlations as inthe known method by Thorn et al. Since the calculation of crosscorrelations is by far the most time-consuming processing step, thisaspect of the present invention results in an enormous improvement ofprocessing efficiency and a much increased speed of operation.

[0029] For the sake of completeness, reference is made to the book‘Imaging Industrial Flows: Applications of Electrical ProcessTomography’ by A. Plaskowski, M. S. Beck, R. Thorn and T. Dyakowski, IOPPublishing, 1995. With reference to future developments in flow velocityimaging, on page 197 of the book the following imprecise statement ismade: ‘Basic research will be focused on: Considering the relativemerits of cross correlation of tomographic view data sometimes followedby reconstruction, compared with cross correlation of reconstructedimage pixel data’. However, the book does not disclose how that is donein practice.

[0030] Further it is noted, that there are many other methods known todetermine a flow property, and in relation to the present invention onesuch method is discussed in detail. Reference is made to U.S. Pat. No.4,228,353, which publication relates to methods for determining amass-flow rate of a fluid. However, these methods rely oncross-correlation X-ray tomography, in contrast to the present inventionwherein a capacitance meter is used. The methods as described in the USApatent publication comprise the determination of density images and flowvelocity profiles.

[0031] In X-ray tomography, a transmitted X-ray intensity is measuredalong various well-defined ray paths. The first processing step of themethods according to the USA patent publication is to calculate anaverage density along a ray path from the measured transmitted X-rayintensity. For the subsequent determination of a flow velocity profile,two methods are considered:

[0032] (i) first calculating density images from the average densities,followed by cross correlation of pixel data; and

[0033] (ii) first calculating cross correlations of average densities,which are used in the calculation of cross correlations of pixel data.

[0034] Therefore, both methods differ from the method of the presentinvention.

[0035] The present invention further relates to calibrating acapacitance meter. A useful calibration method will improve therobustness of operating a capacitance meter in practice. Under operatingconditions, environmental influences act upon the annular capacitancesensor and may influence the measurements; examples of suchenvironmental influences are temperature changes, pressure changes,external forces, changes in the electrode arrangement, deposition ofmaterials on the electrodes or in the space probed by the annularcapacitance sensor. Capacitance measurements, in particular forcross-correlation capacitance tomography, have to be performed withsufficient precision in order to provide useful data. Therefore a methodis needed that allows correcting for environmental influences by anefficient calibration of the capacitance meter. Applicant has found thatand how a relationship between capacitances measured by an annularcapacitance sensor can be utilised in a new method for correctingmeasured capacitances.

[0036] If the conduit inside an annular capacitance sensor is filledwith a calibration fluid having a known dielectric property, say havingthe dielectric constant ε, then calibration capacitances can be measuredbetween pairs of sensor electrodes of the annular capacitance sensor. Ifthe calibration measurements are repeated after some time using acalibration fluid having the same dielectric property, in general achange in measured calibration capacitances will be noticed, due toenvironmental influences.

[0037] During normal operation of an annular capacitance sensor,however, it will be filled with a test fluid having an unknowndielectric property, and it is the purpose of the capacitance sensor todetermine the unknown dielectric property by measuring testcapacitances. Therefore, it will be clear that a method for correctingthe measured test capacitances is needed in order to account for theeffect of environmental influences.

[0038] Thus, furthermore is provided a new method for providingcorrected capacitances using an annular capacitance sensor fordetermining a dielectric property of a test fluid in a conduit, whichcapacitance sensor comprises at least four sensor electrodes arrangedaround the circumference of the conduit, the method comprising the stepsof:

[0039] filling the conduit with the test fluid;

[0040] selecting a set of measurement capacitors, wherein a measurementcapacitor is formed by two measurement electrodes, and wherein ameasurement electrode consists either of a single sensor electrode or ofat least two interconnected sensor electrodes;

[0041] measuring a test capacitance of each measurement capacitor;

[0042] wherein the method further comprises the steps of

[0043] interrupting the measurement at certain moments in time;

[0044] filling the conduit with a calibration fluid having a knowndielectric property;

[0045] selecting a set of calibration capacitors, wherein a calibrationcapacitor is formed by two calibration electrodes, and wherein acalibration electrode consists either of a single sensor electrode or ofat least two interconnected sensor electrodes;

[0046] measuring a calibration capacitance of each calibrationcapacitor; and

[0047] determining corrected capacitances from the test capacitances andthe calibration capacitances by using a relationship between thecalibration capacitances and the known electric property of thecalibration fluid.

[0048] Reference is made to the article by D. G. Lampard and R. D.Cutkosky in Proc. Instr. of Electrical Engineers part C, vol. 196C, TheInstitute of Electrical Engineers, Monograph No. 351 M, January 1960. Inthis article, a theorem in electrostatics is discussed, which in thefollowing will be referred to as the Thompson-Lampard theorem.

[0049] The Thompson-Lampard theorem relates to a conducting cylindricalshell, which is subdivided into four mutually isolated electrodes bynarrow gaps parallel to the axis of the cylindrical shell. If thecylindrical shell is filled with a material having a known dielectricconstant ε, the following relationship holds:

e ^(−πC) ^(₁) ^(/ε) +e ^(−πC) ^(₂) ^(/ε)=1

[0050] wherein

[0051] C₁ is the capacitance per unit length of a capacitor formed bytwo non-neighbouring electrodes;

[0052] C₂ is the capacitance per unit length of a capacitor formed bythe two remaining electrodes; and

[0053] ε is the dielectric constant, which for a homogeneous material isthe product of the dielectric constant of the vacuum ε₀, and a relativedielectric constant ε_(r) that is a property of the material.

[0054] The Thompson-Lampard theorem provides a relationship between theknown dielectric property of a material, e.g. a calibration fluid, andmeasured calibration capacitances. The Thompson-Lampard theorem therebyprovides the basis for the method of the present invention for providingcorrected capacitances for a rest fluid. In practice, a modification ofthe Thompson-Lampard theorem may be needed, in order to account forspecifics of the practical situation, e.g. dimensions of electrode gaps,the presence of other dielectric materials than the calibration fluid,such as a conduit wall, in the vicinity of the sensor electrodes.

[0055] For example, a generalised form of the Thompson-Lampard theoremis

e ^(−πC) ^(₁) ^(/ε) +e ^(−πC) ^(₂) ^(/ε) =c,

[0056] wherein the constant c equals 1 under ideal circumstances, butmay deviate from 1 in a practical situation. The deviation from idealitycan in part be caused by the electrode arrangement in a practicalannular capacitance sensor (e.g. size of gaps between electrodes, lengthof the electrodes, the presence of guard electrodes, electric screens ordielectric materials in the vicinity of the electrodes), and in part byenvironmental influences. If necessary, deviations due to electrodearrangement can be estimated, or accounted for by comparison withmeasurements in which other environmental influences have been excluded,e.g. factory calibration measurements.

[0057] The present invention will now be described by way of example inmore detail with reference to the drawings, wherein

[0058]FIG. 1 shows schematically a side view of a conduit provided witha capacitance meter comprising two annular capacitance sensors inaccordance with the present invention; and

[0059]FIG. 2 shows, on a different scale than FIG. 1, schematically across-section of the conduit of FIG. 1 along the line I-I.

[0060] Reference is now made to FIGS. 1 and 2. The conduit 1 is providedwith upstream and downstream annular capacitance sensors, 2 a and 2 b,separated by the distance L. Each annular capacitance sensor in thisexample comprises eight electrodes, 11 a, . . . , 18 a and 11 b, . . . ,18 b, which are uniformly distributed around the circumference of theconduit 1.

[0061] Normal operation of the cross-correlation capacitance meter asschematically depicted in FIGS. 1 and 2, will now be described, whereina multi-component fluid is flowing through the conduit 1 in thedirection of the arrow 20.

[0062] At first, a set of measurement capacitors is selected. In thisexample, a measurement capacitor is formed by a pair of single sensorelectrodes, and all 8*(8−1)/2=28 possible pairs of single sensorelectrodes at the upstream sensor are selected, i.e. the pairs (11 a, 12a); (11 a, 13 a); . . . ; (11 a, 18 a); (12 a, 13 a); . . . ; (12 a, 18a); . . . ; (17 a, 18 a), as well as all 28 pairs of single sensorelectrodes at the downstream sensor, i.e. the pairs (11 b, 12 b); (11 b,13 b); . . . ; (11 b, 18 b); (12 b, 13 b); . . . ; (12 b, 18 b); . . . ;(17 b, 18 b). In this way, a single sensor electrode forms part of anumber of measurement capacitors.

[0063] Next, a time interval is selected, and the capacitance of each ofthe selected measurement capacitors is measured at different momentsduring the time interval. Every capacitance measurement is probing thedielectric properties of the fluid that is flowing at that moment in thespace probed by the respective pair of electrodes. E.g. the capacitanceof the pair (11 a, 12 a) is measured at several moments in time duringthe interval. It may be desirable to measure more than one capacitanceat the same moment in time, for example the capacitance of allmeasurement capacitors that include a particular sensor electrode suchas (11 a, 12 a); (11 a, 13 a); (11 a, 14 a); . . . ; (11 a, 18 a).

[0064] The capacitances measured at the upstream sensor at a certaintime are denoted by C_(u,i)(t′), and the capacitances measured at thedownstream sensor are denoted by C_(d,j)(t′); (i,j=1, . . . , 28; and t′is a time in the time interval), wherein i and j refer to the respectivepair of electrodes at the upstream and downstream sensors.

[0065] Next, cross correlations between capacitances measured during thetime interval at the upstream sensor, and capacitances measured duringthe time interval at the downstream sensor are determined. To this end atime window of duration T in the time interval is selected, and then thecross correlation between the capacitances is calculated using:${\left( {C_{u,i}*C_{d,j}} \right)(t)} = {\frac{1}{T}{\int_{0}^{T}{{C_{d,j}(s)}\quad {C_{u,i}\left( {t - s} \right)}{s}}}}$

[0066] wherein

[0067] (C_(u,i)*C_(d,j))(t) is the cross correlation betweencapacitances at a selected time t,

[0068] s and (t−s) denote times in the time interval, and the othersymbols have the same meaning as given before.

[0069] The capacitance cross correlations form the basis for determininga flow property of the fluid. In addition, the measured capacitances canbe used to calculate an image. To this end a linear method forcalculating the image the such as linear back projection is used.Accordingly, pixel data P_(u,k) and P_(d,l) (k,l=1, . . . , K) forimages provided by the upstream and downstream sensor are calculatedfrom the capacitances C_(u,i) and C_(d,j) (i,j=1, . . . , 28),respectively, by linear operations which can be expressed by thefollowing equations: $\begin{matrix}{{P_{u,k}\left( t^{\prime} \right)} = {\sum\limits_{i = 1}^{28}\quad {a_{ki}{C_{u,i}\left( t^{\prime} \right)}}}} \\{{P_{d,l}\left( t^{\prime} \right)} = {\sum\limits_{j = 1}^{28}\quad {b_{lj}{C_{d,j}\left( t^{\prime} \right)}}}}\end{matrix}$

[0070] wherein

[0071] k,l=1, . . . , K;

[0072] a_(ki) are elements of a time-independent coefficient matrix forcalculating pixel data from capacitances at the upstream sensor; and

[0073] b_(lj) are elements of a time-independent coefficient matrix forcalculating pixel data from capacitances at the downstream sensor.

[0074] Further in accordance with the present invention, crosscorrelations of pixel data are calculated from cross correlations ofmeasured capacitances, wherein the linearity of the pixel datacalculations is utilised: $\begin{matrix}{{\left( {P_{u,k}*P_{d,l}} \right)(t)} = {\frac{1}{T}{\int_{0}^{T}{{P_{d,l}(s)}\quad {P_{u,k}\left( {t - s} \right)}{s}}}}} \\{= {\frac{1}{T}{\int_{0}^{T}{\underset{j = 1}{\overset{28}{\sum\quad}}\quad {b_{lj}{C_{d,j}(s)}{\sum\limits_{i = 1}^{28}\quad {a_{ki}{C_{u,i}\left( {t - s} \right)}{s}}}}}}}} \\{= {\frac{1}{T}\underset{{j = 1}\quad}{\overset{28\quad}{\sum\quad}}\quad {\sum\limits_{i = 1}^{28}\quad {b_{lj}a_{ki}{\int_{0}^{T}{{C_{d,j}(s)}\quad {C_{u,i}\left( {t - s} \right)}{s}}}}}}}\end{matrix}$ Therefore:  ${\left( {P_{u,k}*P_{d,l}} \right)(t)} = {\underset{{j = 1}\quad}{\overset{28\quad}{\sum\quad}}\quad {\sum\limits_{i = 1}^{28}\quad {b_{lj}{a_{ki}\left( {C_{u,i}*C_{d,j}} \right)}{(t).}}}}$

[0075] Thus, after calculating 28*28=784 cross correlations of all pairsof capacitances measured at the upstream and downstream sensors, allcross correlations of pixel data can be calculated therefrom by linearoperations.

[0076] Using cross correlations of pixel data, various flow propertiesof a fluid can be determined. For example, a flow velocity profile canbe determined. To determine a flow velocity profile, fluid transit timesτ_(kl)(T) between image pixels P_(u,k) at the upstream sensor andP_(d,l) at the downstream sensor are determined by finding the maximumof the cross correlation between the respective pixel data as a functionof time,${\tau_{kl}(T)} = {\max\limits_{0 \leq t \leq T_{\max}}{\left( {P_{u,k}*P_{d,l}} \right)\left( {t,T} \right)}}$

[0077] wherein

[0078] T_(max) is the maximum time window length for time correlation;and the other symbols have the same meaning as given before.

[0079] From the fluid transit times, a fluid flow velocity v_(kl)between pixels P_(u,k) and P_(d,l) can be determined by${{v_{kl}(T)} = \frac{L}{\tau_{kl}(T)}},$

[0080] wherein L is the distance between the upstream and downstreamsensors, eventually corrected in order to take an actual distancebetween pixels into account; and the other symbols have the same meaningas given before.

[0081] The data set formed by all values of v_(kl) (k,l=1, . . . , K) isreferred to as a flow velocity profile. A subset of this flow velocityprofile is the special flow velocity profile which is formed by allvalues of v_(kl), wherein k=1, and k=1, . . . , K, which special flowprofile represents the flow component that is parallel to the axis ofthe conduit.

[0082] If the fluid is a multi-component fluid, other flow properties ofinterest can be determined, if in addition to a flow velocity profilealso an image of the fluid has been calculated. In the image, pixels canbe ascribed to a single one of the components based on the value of thepixel data. By selecting all pixels that have been ascribed to a singlecomponent, together with a flow velocity profile the volumetric flowrate of that component can be determined. If the density of thecomponent is known, also a mass flow rate of that component can bestraightforwardly determined. It will be clear, that a volumetric flowrate and/or a mass flow rate can also be determined in case the fluidconsists of only a single component.

[0083] Preferably, the capacitances C_(u,i) and C_(d,j) are measured inaccordance with the method for providing corrected capacitances of thepresent invention.

[0084] The electrodes in the example of FIG. 1 are arranged on the outersurface 22 of the conduit, however, they may also be arranged in theconduit wall 24, or at the inner surface 26, and they may be covered bya protecting material (not shown). Preferably, all electrodes of anannular capacitance sensor have the same length in axial direction ofthe conduit. A capacitance meter may comprise additional components tothose shown in FIGS. 1 and 2, for example additional annular capacitancesensors for selecting a different distance between upstream anddownstream annular capacitance sensors, an electric screen, guardelectrodes, dielectric filler material, data processing means, datacommunication means, power supply means, or a housing.

[0085] Now the calibration method in accordance with the presentinvention is discussed, and reference is made to the annular capacitancesensor 2 a of FIGS. 1 and 2. During normal operation of the annularcapacitance sensor, the conduit 1 is filled with a fluid, wherein adielectric property of the fluid is being determined based oncapacitances measured by the annular capacitance sensor 2 a. In thefollowing, this fluid will be referred to as the test fluid. Normally,the test fluid will flow through the conduit. A set of measurementcapacitors is selected, normally by selecting all 28 possible pairs ofsingle sensor electrodes. The capacitance of a measurement capacitorformed by a pair of sensor electrodes is influenced by the dielectricproperties of a fluid in the space that is probed by the pair of sensorelectrodes. Further, the measured test capacitance is influenced byenvironmental influences.

[0086] To correct for the environmental influences a method of using anannular capacitance sensor advantageously comprises a calibration stepin order to provide corrected test capacitances. To this end, accordingto the present invention the flow of the test fluid through thecapacitance meter is interrupted, and the fluid is removed from the areathat is probed by the annular capacitance sensor. This area is thenfilled with a calibration fluid with a known dielectric property,preferably with a homogeneous fluid having a homogeneous dielectricconstant ε. The calibration fluid can be a liquid or a gas, e.g. air, aninert gas, or a gas at decreased pressure (‘vacuum’).

[0087] Next, a set of calibration capacitors is selected. To this end,the eight sensor electrodes are subdivided into four consecutivesections [S1; S2; S3; S4], e.g. [(11 a); (12 a); (13 a,14 a,15 a); (16a,17 a,18 a)]. Numbers between parentheses refer to those sensorelectrodes in FIG. 1 that are part of the respective section. All sensorelectrodes that belong to a particular section form, wheninterconnected, a calibration electrode. A first calibration capacitoris selected by selecting two non-neighbouring calibration electrodes.According to the above example, one calibration electrode is formed bythe sensor electrode (11 a), and the other calibration electrode isformed by the interconnected sensor electrodes (13 a,14 a,15 a). Asecond calibration capacitor is selected to be formed by the remainingtwo calibration electrodes, i.e. (12 a) and (16 a,17 a,18 a). It will beclear, that and how other pairs of a first and a second calibrationcapacitor can be selected by using different subdivisions of the sensorelectrodes into consecutive sections, e.g. [(11 a,12 a); (13 a,14 a);(15 a,16 a); (17 a,18 a)], or [(11 a); (12 a,13 a); (14 a,15 a); (16a,17 a,18 a)]. If the set consisting of all possible calibrationcapacitors is selected accordingly, it will be clear, that this set ofcalibration capacitors differs from the set of measurement capacitors.

[0088] For a selected pair of first and second calibration capacitors, acalibration capacitance C_(c,1) of the first capacitor and a calibrationcapacitance C_(c,2) of the second calibration capacitor is measured. Ifa plurality of pairs of first and second calibration capacitors isselected, a plurality of pairs (C_(c,1),C_(c,2)) is measured.

[0089] The calibration capacitances are then converted to calibrationcapacitances per unit length by taking into account the length of theelectrodes. For every such pair of calibration capacitances per unitlength, a relationship based on the Thompson-Lampard theorem must hold.If known deviations from ideality can be accounted for, a modificationof the Thompson-Lampard theorem is used. In a practical situation the(modified) Thompson-Lampard theorem will not be precisely fulfilled, dueto environmental influences. Therefore, by measuring a plurality ofpairs of calibration capacitances per unit length a system of equationsis provided that are not precisely fulfilled. For this system ofequations an optimal solution is determined. It may be advantageous tocompare the optimal solution with optimal solutions that may have beendetermined during previous calibration steps, e.g. during an initialcalibration step in the factory. Further, if there is sufficientsymmetry in the size and arrangement of the calibration electrodes, thetheorem may be reduced to the requirement that the both values of a pairof calibration capacitances must be equal to a certain value.

[0090] After all measurements of calibration capacitances have beenperformed, the calibration step can be finished. The calibration fluidis removed from the annular capacitance sensor and the conduit can againbe filled with test fluid. The optimal solution that has been determinedis subsequently used to determine the correction that is needed for testcapacitances, that are measured by the annular capacitance sensor whenfilled with a test fluid. In particular, all capacitances C_(u,i) andC_(d,j) that are measured in a method for determining a flow property ofthe a fluid are with advantage corrected in this way.

[0091] A practical requirement that is for example relevant to the oilindustry concerns the need for measurement devices that can be operatedremotely in e.g. a wellbore or in a subsea installation. The presentinvention therefore also relates to a capacitance meter which comprisesmeans for remote operation, which suitably includes means for telemetryand/or remote power supply. Telemetry is a specific aspect of remoteoperation, which is for example needed for control of the capacitancemeter and for the data communication. The supply of the required powerfor the operation of the capacitance meter is another aspect of remoteoperation. It is often undesirable that a capacitance meter is providedwith a cable that runs through the wellbore up to the surface. However,in a wellbore, telemetry and/or remote power supply can for example beprovided via the casing and/or tubing that is arranged in the wellbore.To this end, the means for telemetry and/or remote power supply suitablycomprises an inductive coupler which uses an alternating electromagneticfield for the transfer of data and/or electrical power between thecapacitance meter and the casing or tubing. The capacitance meter mayfurther comprise other electronic components, for example means forpower regulation and storage, which can include a rechargeable batteryor an ultracapacitor, a data processor, a controller or a communicationinterface.

1. A method for determining a flow property of a fluid flowing through aconduit provided with a capacitance meter comprising an annularcapacitance sensor, wherein the annular capacitance sensor comprises atleast three sensor electrodes, which sensor electrodes are arrangedaround the circumference of the conduit, the method comprising the stepsof: (a) selecting, for the annular capacitance sensor, a set ofmeasurement capacitors, wherein a measurement capacitor is formed by twomeasurement electrodes, and wherein a measurement electrode consistseither of a single sensor electrode or of at least two interconnectedsensor electrodes; (b) measuring a capacitance of each measurementcapacitor, characterized in that the annular capacitance sensor forms anupstream annular capacitance sensor, and in that the capacitance meterfurther comprises a downstream annular capacitance sensor provided withat least three sensor electrodes, which sensor electrodes are arrangedaround the circumference of the conduit, wherein the method furthercomprises the steps of (c) selecting, for the downstream annularcapacitance sensor, a set of measurement capacitors; (d) measuring atseveral moments during a time interval a capacitance of each measurementcapacitor of each annular capacitance sensor; (e) determining crosscorrelations between capacitances measured during the time interval atthe upstream annular capacitance sensor and capacitances measured duringthe time interval at the downstream annular capacitance sensor; and (f)determining the flow property from the cross correlations.
 2. A methodaccording to claim 1, wherein the fluid comprises at least two fluidcomponents, and wherein a fluid property of a fluid component isdetermined.
 3. A method according to claim 1 or 2, wherein the flowproperty is one of a flow velocity profile over a cross-section of theconduit, a volumetric flow rate, or a mass flow rate.
 4. A methodaccording to any one of claims 1-3, wherein the fluid comprises at leasttwo components selected from the group of hydrocarbon oil, water, andnatural gas.
 5. A capacitance meter for determining a flow property of afluid flowing through a conduit, the capacitance meter comprising anupstream and a downstream annular capacitance sensor arranged around theconduit, wherein each annular capacitance sensor comprises at leastthree sensor electrodes, which sensor electrodes are arranged around thecircumference of the conduit, and wherein the capacitance meter isoperated according to the method of any one of claims 1-4.
 6. Acapacitance meter according to claim 5, which capacitance meter issuitable for usage subsea or in a wellbore in the earth in that itfurther comprises means for remote operation.
 7. A capacitance meteraccording to claim 6, wherein the means for remote operation comprisesmeans for telemetry or means for remote power supply.
 8. A method forproviding corrected capacitances using an annular capacitance sensor fordetermining a dielectric property of a test fluid in a conduit, whichcapacitance sensor comprises at least four sensor electrodes arrangedaround the circumference of the conduit, the method comprising the stepsof: filling the conduit with the test fluid; selecting a set ofmeasurement capacitors, wherein a measurement capacitor is formed by twomeasurement electrodes, and wherein a measurement electrode consistseither of a single sensor electrode or of at least two interconnectedsensor electrodes; measuring a test capacitance of each measurementcapacitor; wherein the method further comprises the steps ofinterrupting the measurement at certain moments in time; filling theconduit with a calibration fluid having a known dielectric property;selecting a set of calibration capacitors, wherein a calibrationcapacitor is formed by two calibration electrodes, and wherein acalibration electrode consists either of a single sensor electrode or ofat least two interconnected sensor electrodes; measuring a calibrationcapacitance of each calibration capacitor; and determining correctedcapacitances from the test capacitances and the calibration capacitancesby using a relationship between the calibration capacitances and theknown electric property of the calibration fluid.
 9. A method accordingto claim 8, wherein the step of selecting a set of calibrationcapacitors comprises the following steps selecting four calibrationelectrodes by subdividing the sensor electrodes around the circumferenceinto four consecutive sections, wherein each section comprises either asingle sensor electrode or at least two interconnected sensor electrodesand wherein each section forms a calibration electrode; and selecting afirst and a second calibration capacitor, wherein the first calibrationcapacitor is formed by two non-neighbouring of the four calibrationelectrodes, and wherein the second calibration capacitor is formed bythe remaining two calibration electrodes.
 10. A method according toclaim 9, wherein in the step of determining corrected capacitances arelationship between the calibration capacitance of the firstcalibration capacitor, the calibration capacitance of the secondcalibration capacitor, and the known dielectric property is used.
 11. Amethod according to claim 10, wherein the relationship is theThompson-Lampard theorem, or is based on a modification of theThompson-Lampard theorem.
 12. A capacitance meter for determining adielectric property of a test fluid in a conduit, the capacitance metercomprising an annular capacitance sensor, which annular capacitancesensor comprises at least four sensor electrodes arranged around thecircumference of the conduit, wherein the capacitance meter iscalibrated according to the method of any one of claims 8-11.
 13. Amethod according to any one of claims 1-4, wherein the fluid is a testfluid, wherein each annular capacitance sensor comprises at least foursensor electrodes, and wherein the capacitances determined in step (b)are capacitances that have been corrected according to the method of anyone of claims 8-11.
 14. A capacitance meter for determining a flowproperty of a fluid flowing through a conduit, the capacitance metercomprising an upstream and a downstream annular capacitance sensorarranged around the conduit, wherein each annular capacitance sensorcomprises at least four sensor electrodes, which sensor electrodes arearranged around the circumference of the conduit, and wherein thecapacitance meter is operated according to the method of claim 13.